One-way valves for dispensing fluids from compressible containers, such as tubes, are known. For example WO2011/127610 A1 describes a one-way valve for a tube. The construction of this valve with a flat disc-shaped valve member and a particularly dimensioned head space above the flat disc results in a rather strict limitation of the flow of the product to be dispensed, which is a desired effect of this valve, but may not be advantageous for other containers for which a less restricted flow may be desirable. An essential effect of a one-way valve is to avoid the sucking in of air into the container or tube, respectively, when compression of the container is released and dispensing is stopped. Thus the one-way valve will minimize reactions of air and in particular oxygen with the contents of the container. Further, when air is not allowed to enter the container by the one-way valve it is avoided that the container regains its original shape and thus the increasing deformation of the container gives an indication of the contents remaining in the container. EP 850 177 B1 shows a self-closing closure with a closure membrane having a concave shaped, slitted closure head, which bursts open upon pressure on the container and which is designed to allow air to enter the container after dispensing and which is thus not a one-way valve for preventing the entrance of air into the container. Thus, known one-way valves do permit only low flow rates—which can be very well suited for small tubes in particular in the pharmaceutical field or such closures—if suited for larger amounts of liquid to be dispensed—do not prevent the entrance of air into the container.